Because the question is lacking specifics, this answer is lacking specifics.
I need to know how much length the two whip antennas have, and how much gap should there be between them to make them work as a dipole antenna?
The appropriate length is frequency dependent, so you should choose a length that is appropriate for the frequency that you are looking to receive.
The gap should be as small as practical. I have no idea of the appropriateness of the antenna to your need since you omit it. Suffice it to say that it's not critical and shouldn't be high up on a list of concerns for any practical antenna build.
How are all the three antennas connected in this rabbit ears antenna?
In my experience, the VHF and UHF antennas are connected via separate transmission lines to the TV. The VHF using coax and an F-style connector (IIRC) and the UHF using twin-lead and a balun. Or maybe the other way around. you can google to figure which is which.
The rabbit ears are 2 elements of a single VHF antenna (yes, a dipole!), one of which is connected to the shield of the coax transmission line, the other of which is connected to the center conductor.
Each end of the UHF loop is connected to one of the twin-lead wires.
I'm sorry there isn't more to share here, but that's mainly a result of the vagueness of the question.